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APPENDIX B –ELECTROMAGNETIC RADIATION FROM A DIPOLE ANTENNA 25 The prediction of electromagnetic wave propagation by James Clerk Maxwell, circa 1865, and subsequent experimental verification by Heinrich Hertz, circa 1887, is singularly, the most significant achievement of the 19 th century. Prior to Maxwell's prediction and extensive documentation in "A Treatise on Electricity and Magnetism" (1873), electricity and magnetism consisted exclusively of isolated experimental observation by several noted scientists, among them: Coulomb, Ampere, Gauss, Volta and Faraday. Maxwell used his extraordinary insight and mathematical proficiency to produce a mathematically and scientifically definitive work which unified the subjects of electricity and magnetism and established the foundation for the study of electromagnetics. Maxwell recognized the coupling and symmetry of the curl equations and concluded that the previously independent fields were, in fact, related. Maxwell's Curl Equations for a charge free region: The curl of a vector field may be physically interpreted as a mathematical operation which finds its source. Therefore, the curl of the electric field vector, i.e., , finds its source as the time derivative of the magnetic field vector; and conversely, the curl of the magnetic field vector, i.e., , finds its source as the time derivative of the electric field vector. One may extend the observations and further conclude that there exists a repeated, or periodic, cause-and-effect relationship between the coupled vector fields. The action of the related fields may now be extended using a practical example. Consider Figure B-1, where a simple dipole element exists along the z-axis with current, I. The current is the result of a sinusoidal voltage source at the input terminals of the dipole. At the initial instant of application of the excitation source, the H-field is circumferential and lies in a plane which is normal to the axis of the diode. The current is assumed constant over the length of the diode and produces a magnetic field around the dipole element in accordance with Maxwell's equation: Recall from the curl operation, the H-field has found its source, i.e., the current density along the dipole element, and that the geometrical relationship of the curl and its source is orthogonal. As stated earlier, the time changing magnetic field vector – the source – produces an electric field vector in accordance with Maxwell's equation for a charge free region: 25 The explanation is not scientifically or mathematically accurate; it is intended to offer a physical interpretation of the method by which electromagnetic waves originate in the proximity of a conductor carrying a sinusoidal current, and to subsequently propagate from the conductor. t E H t H E ¶ ¶ = ´ Ñ ¶ ¶ - = ´ Ñ ! ! ! ! e µ E ! ´ Ñ H ! ´ Ñ c J H ! ! = ´ Ñ Figure B-1: Simple Dipole with Sinusoidal Excitation (upon application of excitation, the current produces the H-field) Microstrip Antenna Design 26 www.cadence.com/go/awr

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